This paper presents a CFD-based simulation method for air/water and water/dodecane Taylor flows through an axisymmetric microchannel with a circular cross-sectional area. A systematic analysis is conducted by exploring the effects of different superficial velocities and apparent viscosities on the hydrodynamics of a slug flow regime. A concentric junction is employed to make bubbles of air in a continuous flow of water and slugs of water in a continuous flow of dodecane oil. A time-history study is conducted to predict the air-bubble and water-slug evolution processes, in particular at the moment of slug breakup. The results show that the larger apparent viscosity ratio of phases involved in the liquid-liquid flow generates a more stable interface. However, the liquid slug length is less and film thickness is slightly larger in liquid-liquid compared to gas-liquid flow. Furthermore, variations in gas and liquid holdups are correlated by the superficial velocity ratio. The numerical analysis developed in this paper is in good agreement with the correlations and data in the literature.